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Statistics LibreTexts

8.2: Loops

  • Page ID
    3987
  • The description I gave earlier for how a script works was a tiny bit of a lie. Specifically, it’s not necessarily the case that R starts at the top of the file and runs straight through to the end of the file. For all the scripts that we’ve seen so far that’s exactly what happens, and unless you insert some commands to explicitly alter how the script runs, that is what will always happen. However, you actually have quite a lot of flexibility in this respect. Depending on how you write the script, you can have R repeat several commands, or skip over different commands, and so on. This topic is referred to as flow control, and the first concept to discuss in this respect is the idea of a loop. The basic idea is very simple: a loop is a block of code (i.e., a sequence of commands) that R will execute over and over again until some termination criterion is met. Looping is a very powerful idea. There are three different ways to construct a loop in R, based on the while, for and repeat functions. I’ll only discuss the first two in this book.

    8.2.1 The while loop

    A while loop is a simple thing. The basic format of the loop looks like this:

     while ( CONDITION ) {
            STATEMENT1
            STATEMENT2
            ETC
         }

    The code corresponding to CONDITION needs to produce a logical value, either TRUE or FALSE. Whenever R encounters a while statement, it checks to see if the CONDITION is TRUE. If it is, then R goes on to execute all of the commands inside the curly brackets, proceeding from top to bottom as usual. However, when it gets to the bottom of those statements, it moves back up to the while statement. Then, like the mindless automaton it is, it checks to see if the CONDITION is TRUE. If it is, then R goes on to execute all … well, you get the idea. This continues endlessly until at some point the CONDITION turns out to be FALSE. Once that happens, R jumps to the bottom of the loop (i.e., to the } character), and then continues on with whatever commands appear next in the script.

    To start with, let’s keep things simple, and use a while loop to calculate the smallest multiple of 17 that is greater than or equal to 1000. This is a very silly example since you can actually calculate it using simple arithmetic operations, but the point here isn’t to do something novel. The point is to show how to write a while loop. Here’s the script:

    ## --- whileexample.R
    x <- 0
    while ( x < 1000 ) {
      x <- x + 17
    }
    print( x )

    When we run this script, R starts at the top and creates a new variable called x and assigns it a value of 0. It then moves down to the loop, and “notices” that the condition here is x < 1000. Since the current value of x is zero, the condition is true, so it enters the body of the loop (inside the curly braces). There’s only one command here135 which instructs R to increase the value of x by 17. R then returns to the top of the loop, and rechecks the condition. The value of x is now 17, but that’s still less than 1000, so the loop continues. This cycle will continue for a total of 59 iterations, until finally x reaches a value of 1003 (i.e., 59×17=1003). At this point, the loop stops, and R finally reaches line 5 of the script, prints out the value of x on screen, and then halts. Let’s watch:

    source( "./rbook-master/scripts/whileexample.R" )
    ## [1] 1003

    Truly fascinating stuff.

    8.2.2 The for loop

    The for loop is also pretty simple, though not quite as simple as the while loop. The basic format of this loop goes like this:

     for ( VAR in VECTOR ) {
            STATEMENT1
            STATEMENT2
            ETC
         }

    In a for loop, R runs a fixed number of iterations. We have a VECTOR which has several elements, each one corresponding to a possible value of the variable VAR. In the first iteration of the loop, VAR is given a value corresponding to the first element of VECTOR; in the second iteration of the loop VAR gets a value corresponding to the second value in VECTOR; and so on. Once we’ve exhausted all of the values in VECTOR, the loop terminates and the flow of the program continues down the script.

    Once again, let’s use some very simple examples. Firstly, here is a program that just prints out the word “hello” three times and then stops:

    ## --- forexample.R
    for ( i in 1:3 ) {
      print( "hello" )
    }

    This is the simplest example of a for loop. The vector of possible values for the i variable just corresponds to the numbers from 1 to 3. Not only that, the body of the loop doesn’t actually depend on i at all. Not surprisingly, here’s what happens when we run it:

    source( "./rbook-master/scripts/forexample.R" )
    ## [1] "hello"
    ## [1] "hello"
    ## [1] "hello"

    However, there’s nothing that stops you from using something non-numeric as the vector of possible values, as the following example illustrates. This time around, we’ll use a character vector to control our loop, which in this case will be a vector of words. And what we’ll do in the loop is get R to convert the word to upper case letters, calculate the length of the word, and print it out. Here’s the script:

    ## --- forexample2.R
    
    #the words_
    words <- c("it","was","the","dirty","end","of","winter")
    
    #loop over the words_
    for ( w in words ) {
    
      w.length <- nchar( w )     # calculate the number of letters_
      W <- toupper( w )          # convert the word to upper case letters_
      msg <- paste( W, "has", w.length, "letters" )   # a message to print_
      print( msg )               # print it_
      
    }

    And here’s the output:

    source( "./rbook-master/scripts/forexample2.R" )
    
    ## [1] "IT has 2 letters"
    ## [1] "WAS has 3 letters"
    ## [1] "THE has 3 letters"
    ## [1] "DIRTY has 5 letters"
    ## [1] "END has 3 letters"
    ## [1] "OF has 2 letters"
    ## [1] "WINTER has 6 letters"

    Again, pretty straightforward I hope.

    8.2.3 A more realistic example of a loop

    To give you a sense of how you can use a loop in a more complex situation, let’s write a simple script to simulate the progression of a mortgage. Suppose we have a nice young couple who borrow $300000 from the bank, at an annual interest rate of 5%. The mortgage is a 30 year loan, so they need to pay it off within 360 months total. Our happy couple decide to set their monthly mortgage payment at $1600 per month. Will they pay off the loan in time or not? Only time will tell.136 Or, alternatively, we could simulate the whole process and get R to tell us. The script to run this is a fair bit more complicated.

    ## --- mortgage.R
    
    # set up
    month <- 0        # count the number of months
    balance <- 300000 # initial mortgage balance
    payments <- 1600  # monthly payments
    interest <- 0.05  # 5% interest rate per year
    total.paid <- 0   # track what you've paid the bank
    
    # convert annual interest to a monthly multiplier
    monthly.multiplier <- (1+interest) ^ (1/12)
    
    # keep looping until the loan is paid off...
    while ( balance > 0 ) {
      
      # do the calculations for this month
      month <- month + 1  # one more month
      balance <- balance * monthly.multiplier  # add the interest
      balance <- balance - payments  # make the payments
      total.paid <- total.paid + payments # track the total paid
      
      # print the results on screen
      cat( "month", month, ": balance", round(balance), "\n")
      
    } # end of loop
    
    # print the total payments at the end
    cat("total payments made", total.paid, "\n" )

    To explain what’s going on, let’s go through it carefully. In the first block of code (under #set up) all we’re doing is specifying all the variables that define the problem. The loan starts with a balance of $300,000 owed to the bank on month zero, and at that point in time the total.paid money is nothing. The couple is making monthly payments of $1600, at an annual interest rate of 5%. Next, we convert the annual percentage interest into a monthly multiplier. That is, the number that you have to multiply the current balance by each month in order to produce an annual interest rate of 5%. An annual interest rate of 5% implies that, if no payments were made over 12 months the balance would end up being 1.05 times what it was originally, so the annual multiplier is 1.05. To calculate the monthly multiplier, we need to calculate the 12th root of 1.05 (i.e., raise 1.05 to the power of 1/12). We store this value in as the monthly.multiplier variable, which as it happens corresponds to a value of about 1.004. All of which is a rather long winded way of saying that the annual interest rate of 5% corresponds to a monthly interest rate of about 0.4%.

    Anyway… all of that is really just setting the stage. It’s not the interesting part of the script. The interesting part (such as it is) is the loop. The while statement on tells R that it needs to keep looping until the balance reaches zero (or less, since it might be that the final payment of $1600 pushes the balance below zero). Then, inside the body of the loop, we have two different blocks of code. In the first bit, we do all the number crunching. Firstly we increase the value month by 1. Next, the bank charges the interest, so the balance goes up. Then, the couple makes their monthly payment and the balance goes down. Finally, we keep track of the total amount of money that the couple has paid so far, by adding the payments to the running tally. After having done all this number crunching, we tell R to issue the couple with a very terse monthly statement, which just indicates how many months they’ve been paying the loan and how much money they still owe the bank. Which is rather rude of us really. I’ve grown attached to this couple and I really feel they deserve better than that. But, that’s banks for you.

    In any case, the key thing here is the tension between the increase in balance on and the decrease. As long as the decrease is bigger, then the balance will eventually drop to zero and the loop will eventually terminate. If not, the loop will continue forever! This is actually very bad programming on my part: I really should have included something to force R to stop if this goes on too long. However, I haven’t shown you how to evaluate “if” statements yet, so we’ll just have to hope that the author of the book has rigged the example so that the code actually runs. Hm. I wonder what the odds of that are? Anyway, assuming that the loop does eventually terminate, there’s one last line of code that prints out the total amount of money that the couple handed over to the bank over the lifetime of the loan.

    Now that I’ve explained everything in the script in tedious detail, let’s run it and see what happens:

    source( "./rbook-master/scripts/mortgage.R" )
    ## month 1 : balance 299622 
    ## month 2 : balance 299243 
    ## month 3 : balance 298862 
    ## month 4 : balance 298480 
    ## month 5 : balance 298096 
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    ## month 356 : balance -1554 
    ## total payments made 569600

    So our nice young couple have paid off their $300,000 loan in just 4 months shy of the 30 year term of their loan, at a bargain basement price of $568,046 (since 569600 - 1554 = 568046). A happy ending!